The US vice-president, Dick Cheney, today attacked Russia's invasion of Georgia, describing it as "an illegitimate, unilateral attempt" to change the country's borders, and saying that there were now "grave doubts" about Russia's reliability as an international partner.

In comments likely to further sharpen the division between Moscow and Washington, Cheney said the US was "fully committed" to Georgia – and its efforts to join Nato. "Georgia will be in our alliance," Cheney said, following talks in Tbilisi this morning with Georgia's president, Mikheil Saakashvili.

Cheney's trip, which will see him fly to Ukraine later today, is designed to demonstrate the US's resolve in supporting Georgia, despite its brief and disastrous war with Russia last month, and the continuing occupation of much of the country by Russian troops.

Today Cheney said that the US would remain at Georgia's side "as you work to overcome an invasion of your sovereign territory and an illegitimate, unilateral attempt to change your country's borders by force that has been universally condemned by the free world".

He added: "Russia's actions have cast grave doubts on Russia's intentions and on its reliability as an international partner."

The Bush administration yesterday announced a $1bn (£500m) humanitarian and economic assistance package to rebuild the country's civilian infrastructure, severely damaged by Russian bombardment during last month's brief conflict.

But there was no mention from Cheney today as to whether the US now intends to help Georgia re-equip its battered military, severely mauled during its fight with Russia – a contentious issue that could escalate the standoff in the region between Washington and Moscow.

Instead, Cheney praised Georgia's contribution in Iraq, as the third largest contributor of troops, saying: "Now it is the responsibility of the free world to rally to the side of Georgia." Today Saakashvili said he was committed to the peaceful resolution of Georgia's disputes with the breakaway regions of South Ossetia and Abkhazia, whose independence Moscow recognized last week.

Saakashvili also said that "two thirds of the population of South Ossetia" had been subjected to ethnic cleaning since last month – with Georgians driven and burned out of their homes by South Ossetian militias. "If someone wishes to legalise the results of this ethnic cleansing, this means legalising people's tragedy," Saakashvili said.

Cheney visited Azerbaijan yesterday, in a trip he said was designed to underline America's "deep and abiding interests" in the region. Russia has accused the US of trying to destabilise the situation in the Caucasus – with the prime minister, Vladimir Putin, claiming that Washington both knew about, and took part in, Georgia's offensive last month against South Ossetia.

Today Dmitry Rogozin, Russia's hawkish representative to Nato, warned that Russia would respond angrily if Georgia were ever allowed join the transatlantic military alliance. Rogozin said Moscow would halt cooperation with Nato over Afghanistan. He also described as "insolent" a visit planned for September 15-16 to Tbilisi by Nato's secretary general Jaap de Hoop Scheffer.

The dispatch of Cheney to the area is in itself a message. Cheney leads the hawkish wing of the Bush administration, and has championed taking a tough line with Russia. He is the most senior member of the US administration to visit Georgia so far.

Yesterday Moscow's ambassador to London, Yuri Fedotov, said that Russia would withdraw its troops from the "buffer zone" it has created in Georgia only when they could be replaced by international peacekeepers and once the Georgian government had signed non-aggression pacts with South Ossetia and Abkhazia.

Fedotov said he "deplored" the severe criticism of Russia voiced recently by the prime minister, Gordon Brown, and the foreign secretary, David Miliband. He claimed to have repeatedly warned the Foreign Office about the worsening crisis in Georgia in the weeks leading up to August 7, when the conflict ignited. He said he had been assured that Saakashvili was "under control". The Foreign Office rejected Fedotov's account.

The Russian ambassador was speaking to a group of journalists about the prospects for a deal at a summit next Monday, when the French and current EU president, Nicolas Sarkozy is due to fly to Moscow with the head of the EU commission, José Manuel Barroso, and the European foreign policy head, Javier Solana, to meet Russia's president, Dmitry Medvedev.

"I'm not in a position to anticipate the outcome of Monday's discussion, but if the EU proposes a very clear plan on how to prevent a potential confrontation and further shelling in the territory of South Ossetia ... then it's not difficult to deploy 200 or 400 people in the zones and to allow Russia to withdraw its personnel," Fedotov said.